Recent content by raj123

Normal subgroups?? Normal subgroups?

let me do the first one for you... 18t2-2 = 2(9t2-1) = 2(3t+1)(3t-1). see if you can do the other one.

thanks. that was easy.

xn= e.what are the next steps in this proof?

that will be... (y-1xy)n = y-1xny

i see. how about this.. (y-1xy)(y-1xy) = y-1xyy-1xy = y-1x2y

(y-1xy)2 =y-2x2y2 =y-2+2x2=x2

isn't y-1xy=x since y-1y=e. so o(y-1xy)=o(x).

If G is a group and x, y are in G. Show that o(x) = o(y^-1xy), where o(x) means order of x. thanks

thanks a lot for helping.

so the kernel will be {-1,1}.

so 1 is the identity.

is 4 the identity ? not sure

e is the identity element.

if O:G -> H is a homomorphism , then the kernel of O is the set of all elements a in G such that O(a) = e of H(identity of H).The kernel of a homomorphism is always a subgroup of the domain.